This paper contains an extensive global treatment of radial motions of compressible nonlinearly viscoelastic cylindrical and spherical shells under time-dependent pressures. It furnishes a variety of conditions on a general class of material properties and on the pressure terms ensuring that there are solutions existing for all times, there are unbounded globally defined solutions, there are solutions that blow up in finite time, and there are solutions having the same period as that of the pressure terms. The shells are described by a geometrically exact 2-dimensional theory in which the shells suffer thickness strains as well as the standard stretching of their base surfaces. Consequently their motions are governed by fourth-order systems of semilinear ordinary differential equations. This work shows that there are major qualitative differences between the nonlinear dynamical behaviors of cylindrical and spherical shells.

Forced Radial Motions of Nonlinearly Viscoelastic Shells / Stuart S., Antman; Lacarbonara, Walter. - In: JOURNAL OF ELASTICITY. - ISSN 0374-3535. - STAMPA. - 96:2(2009), pp. 155-190. [10.1007/s10659-009-9203-7]

Forced Radial Motions of Nonlinearly Viscoelastic Shells

LACARBONARA, Walter
2009

Abstract

This paper contains an extensive global treatment of radial motions of compressible nonlinearly viscoelastic cylindrical and spherical shells under time-dependent pressures. It furnishes a variety of conditions on a general class of material properties and on the pressure terms ensuring that there are solutions existing for all times, there are unbounded globally defined solutions, there are solutions that blow up in finite time, and there are solutions having the same period as that of the pressure terms. The shells are described by a geometrically exact 2-dimensional theory in which the shells suffer thickness strains as well as the standard stretching of their base surfaces. Consequently their motions are governed by fourth-order systems of semilinear ordinary differential equations. This work shows that there are major qualitative differences between the nonlinear dynamical behaviors of cylindrical and spherical shells.
2009
blowup of solutions and periodic solutions; bnlowup of solutions and periodic solutions; nonlinear elasticity and viscoelasticity; radial motions of shells; radial motions of shells - time-dependent pressures - nonlinear elasticity and viscoelasticity - blowup of solutions and periodic solutions; time-dependent pressures
01 Pubblicazione su rivista::01a Articolo in rivista
Forced Radial Motions of Nonlinearly Viscoelastic Shells / Stuart S., Antman; Lacarbonara, Walter. - In: JOURNAL OF ELASTICITY. - ISSN 0374-3535. - STAMPA. - 96:2(2009), pp. 155-190. [10.1007/s10659-009-9203-7]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/109484
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